Option C: $I_{CBO}$ Explanation & Concepts: The collector current $I_C$ in a BJT consists of the component derived from the emitter current ($\alpha I_E$) and a small reverse saturation current flowing from the collector to the base due to minority carriers. This leakage current, known as the collector-to-base leakage current with emitter open, is denoted as $I_{CBO}$. Working Principle: In a BJT, the collector-base junction is reverse-biased. Even when $I_E = 0$, thermal energy generates minority carriers that cross the junction, creating the leakage current $I_{CBO}$. When the transistor is active, the total collector current becomes the sum of the controlled current $\alpha I_E$ and this thermally generated leakage $I_{CBO}$. Key Formulas: $I_C = \alpha I_E + I_{CBO}$ — Total collector current in CB configuration; $I_C = \beta I_B + (1 + \beta) I_{CBO}$ — Total collector current in CE configuration Key Points: $\alpha$ is the common-base current gain, typically ranging from 0.95 to 0.99.; $I_{CBO}$ is highly temperature-dependent and can cause thermal runaway in power transistors.; The equation $I_C = \alpha I_E + I_{CBO}$ is derived from the Ebers-Moll model under steady-state conditions. Advantages: Provides a precise model for transistor behavior at the junction level.; Essential for thermal stability analysis in circuit design. Disadvantages: Does not account for non-ideal effects like base-width modulation (Early effect) without further modification. Applications: Circuit simulation software (SPICE models).; Designing biasing circuits for high-temperature applications. Additional Info: Option B ($I_{CEO}$) is the collector-emitter leakage current with base open, where $I_{CEO} = (1 + \beta) I_{CBO}$.. Option D ($eta I_B$) is the component of $I_C$ in a Common Emitter configuration, not the complete equation.. The parameter $I_{CBO}$ is usually in the range of nanoamperes for Silicon and microamperes for Germanium transistors. Answer: C is correct — The total collector current is the sum of the injected carrier component ($\alpha I_E$) and the thermally generated collector-to-base leakage current ($I_{CBO}$). Exam Tip: Remember that leakage currents ($I_{CBO}$ and $I_{CEO}$) double roughly every 10°C in Silicon, which is critical for solving thermal stability problems in power electronics.

ElectricalElectronics

IC = α IE + _____

$I_B$

$I_{CEO}$

$I_{CBO}$

$\beta I_B$

Correct Answer

Concept & PrincipleElectricalElectronics

Option C

$I_{CBO}$

Quick Summary: The collector current $I_C$ in a BJT consists of the component derived from the emitter current ($\alpha I_E$) and a small reverse saturation current flowing from the collector to the base due to minority carriers. This leakage current, known as the collector-to-base leakage current with emitter open, is denoted as $I_{CBO}$.

💡 Explanation

The collector current $I_C$ in a BJT consists of the component derived from the emitter current ( $\alpha I_E$ ) and a small reverse saturation current flowing from the collector to the base due to minority carriers. This leakage current, known as the collector-to-base leakage current with emitter open, is denoted as $I_{CBO}$ .

🔢 Key Formulas

$I_C = \alpha I_E + I_{CBO}$ — Total collector current in CB configuration

$I_C = \beta I_B + (1 + \beta) I_{CBO}$ — Total collector current in CE configuration

⚙️ Working Principle

In a BJT, the collector-base junction is reverse-biased. Even when $I_E = 0$ , thermal energy generates minority carriers that cross the junction, creating the leakage current $I_{CBO}$ . When the transistor is active, the total collector current becomes the sum of the controlled current $\alpha I_E$ and this thermally generated leakage $I_{CBO}$ .

📌 Key Points

▸
$\alpha$ is the common-base current gain, typically ranging from 0.95 to 0.99.
▸
$I_{CBO}$ is highly temperature-dependent and can cause thermal runaway in power transistors.
▸
The equation $I_C = \alpha I_E + I_{CBO}$ is derived from the Ebers-Moll model under steady-state conditions.

✅ Advantages

▸
Provides a precise model for transistor behavior at the junction level.
▸
Essential for thermal stability analysis in circuit design.

❌ Disadvantages / Limitations

▸
Does not account for non-ideal effects like base-width modulation (Early effect) without further modification.

🛠️ Applications / Uses

▸
Circuit simulation software (SPICE models).
▸
Designing biasing circuits for high-temperature applications.

📄 Additional Information

▸
Option B ( $I_{CEO}$ ) is the collector-emitter leakage current with base open, where $I_{CEO} = (1 + \beta) I_{CBO}$ .
▸
Option D ( $\beta I_B$ ) is the component of $I_C$ in a Common Emitter configuration, not the complete equation.
▸
The parameter $I_{CBO}$ is usually in the range of nanoamperes for Silicon and microamperes for Germanium transistors.

📊 Diagram / Illustration

✅

C is correct — The total collector current is the sum of the injected carrier component ( $\alpha I_E$ ) and the thermally generated collector-to-base leakage current ( $I_{CBO}$ ).

Core Concepts Used

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BJT Terminal Currents Leakage Current Transistor Biasing

💡 EXAM TIP

Remember that leakage currents ( $I_{CBO}$ and $I_{CEO}$ ) double roughly every 10°C in Silicon, which is critical for solving thermal stability problems in power electronics.

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